Mysak 



///////////////////// ^ 



Fig. 6 - Two-layer model. The uniform, basic 

 flow Vq is confined to the deep-sea region and 

 to the upper layer. For the east Australian 

 coast region, typical values of the parameters 

 shown are Vq = 100 cm/sec, d^ = 2.5x10'* cm, 

 Do = 5 X 10^ cm, ? = 5 X 10^ cm, d = 2 x 10" cm. 

 p - 1.025 g/cm^, and p' - p = 2.5x lO"'' g/cm''. 



A^Jo(2xT?), < X < ^, 

 N = < (29) 



Ai exphCa/z^Xx-k-t] + Aj exp[-(x-k^)] , -k > I , 

 Z' = -(1/m^) Ai exp[-(a//x)(x-k^)] + A2 exp [-(y- k^)] , x > -t , (30) 



where ^ = xZ-C, x = kx, and v = -ik-i/co. In obtaining Eqs. (29) and (30), we have 

 imposed the boundary conditions |N(0)| < M, N(oo) = 0, and |z'(oo)| < m. Appli- 

 cation of the boundary condition x'(^) = yields Aj = 0; application of the con- 

 tinuity conditions to the upper layer solutions implies the eigenvalue equation 



Jo(2VT) [/3%(l-Ao)- (l+vRo)\'^o] - /3*Ao^ J^(2\^) 



(31) 



where /3* = ^(gd)^^^ (l\f\)-\ \ = d/d^ , and R^ = -Vq/U. We first note that in 

 the limit /3* -» 0(p' - p-*0) and R^ - 0(Vo -»0), Eq. (31) implies that the eigenval- 

 ues are given by the zeros of jg, in agreement with the unstratified case with no 

 basic deep-sea current. However, with stratification and a deep-sea current, 

 Eq. (31) implies that the eigenvalues are quite different, since /3* , A^, , and Rg 

 are each of order unity. The physical reason for this change in the eigenvalues 

 is that the motion of the surface wave 7] in the deep-sea region is now coupled to 

 that of the interfacial wave C' through the conservation equations, so that new 

 modes of oscillation result. Finally, from Eqs. (28) and (31) we observe that the 

 waves are still nondispersive and progress northward at the east coast of a con- 

 tinent which lies in the southern hemisphere. 



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